Variables de décision : Pour une type de centrale $X \in [A,B,C]$, et une heure de la journée $t\in {1,\dots,24}$, on définit : $$ N_t^{(X)} = \text{Nombre de centrales } X \text{allumées à } t\text{ h, (ENTIER)} $$ $$ P_t^{(X)} = \text{Puissance totale produite par les centrales } X \text{ à } t\text{ h, (CONTINUE)} $$ Contraintes : $$ N_t^{(X)} P_{min}^{(X)} \leq P_t^{(X)} \leq N_t^{(X)} P_{max}^{(X)} \text{ , Contraintes sur la puissance totale de chaque centrale} $$ $$ 0 \leq N_t^{(X)} \leq N^{(X)} \text{ , Contraintes sur le nombre de centrales allumées possible} $$ $$ \forall t, \sum_X P_t^{(X)} = D_t \text{ , Contrainte équilibre offre-demande} $$ Objectif : $$ \text{Minimiser} \sum_X \sum_T P_t^{(X)} C_{MWh}^{(X)} $$
Set parameter TokenServer to value "dev.cma.mines-paristech.fr"
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 168 rows, 144 columns and 360 nonzeros
Model fingerprint: 0xf31da896
Variable types: 72 continuous, 72 integer (0 binary)
Coefficient statistics:
Matrix range [1e+00, 4e+03]
Objective range [1e+00, 3e+00]
Bounds range [5e+00, 1e+01]
RHS range [2e+04, 4e+04]
Found heuristic solution: objective 1235375.0000
Presolve removed 162 rows and 139 columns
Presolve time: 0.02s
Presolved: 6 rows, 5 columns, 14 nonzeros
Found heuristic solution: objective 881275.00000
Variable types: 2 continuous, 3 integer (0 binary)
Root relaxation: objective 8.694000e+05, 2 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 869400.000 0 1 881275.000 869400.000 1.35% - 0s
H 0 0 869400.00000 869400.000 0.00% - 0s
0 0 869400.000 0 1 869400.000 869400.000 0.00% - 0s
Explored 1 nodes (2 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)
Solution count 3: 869400 881275 1.23538e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 8.694000000000e+05, best bound 8.694000000000e+05, gap 0.0000%
Coût : 869400.0
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 168 rows, 144 columns and 360 nonzeros
Model fingerprint: 0x635b27b9
Coefficient statistics:
Matrix range [1e+00, 4e+03]
Objective range [1e+00, 3e+00]
Bounds range [5e+00, 1e+01]
RHS range [2e+04, 4e+04]
Presolve removed 153 rows and 99 columns
Presolve time: 0.00s
Presolved: 15 rows, 45 columns, 45 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 8.5266000e+05 1.743750e+04 0.000000e+00 0s
15 8.6940000e+05 0.000000e+00 0.000000e+00 0s
Solved in 15 iterations and 0.01 seconds (0.00 work units)
Optimal objective 8.694000000e+05
Coût : 869400.0
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 168 rows, 144 columns and 360 nonzeros
Model fingerprint: 0x7066cec8
Variable types: 72 continuous, 72 integer (0 binary)
Coefficient statistics:
Matrix range [1e+00, 4e+03]
Objective range [1e+00, 2e+03]
Bounds range [5e+00, 1e+01]
RHS range [2e+04, 4e+04]
Found heuristic solution: objective 1271875.0000
Presolve removed 162 rows and 139 columns
Presolve time: 0.03s
Presolved: 6 rows, 5 columns, 14 nonzeros
Found heuristic solution: objective 987500.00000
Variable types: 2 continuous, 3 integer (0 binary)
Found heuristic solution: objective 985950.00000
Root relaxation: objective 9.787500e+05, 2 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 978750.000 0 1 985950.000 978750.000 0.73% - 0s
H 0 0 978900.00000 978750.000 0.02% - 0s
0 0 978750.000 0 1 978900.000 978750.000 0.02% - 0s
Explored 1 nodes (2 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)
Solution count 4: 978900 985950 987500 1.27188e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 9.789000000000e+05, best bound 9.789000000000e+05, gap 0.0000%
Coût : 978900.0
Pour ce problème on modifie les variables de décisions et on y adapte les contraintes.
Variables de décision : Pour une type de centrale $X \in [A,B,C]$, et une heure de la journée $t\in {1,\dots,24}$, on définit : $$ N_t^{(X)} = \text{Nombre de centrales } X \text{allumées à } t\text{ h, (ENTIER)} $$ $$ N_{start,t}^{(X)} = \text{Nombre de centrales } X \text{démarrées à } t\text{ h, (ENTIER)} $$ $$ P_t^{(X)} = \text{Puissance totale produite par les centrales } X \text{ à } t\text{ h, (CONTINUE)} $$ Contraintes (par convention $N_{-1}^{(X)}=0$): $$ N_t^{(X)} P_{min}^{(X)} \leq P_t^{(X)} \leq N_t^{(X)} P_{max}^{(X)} \text{ , Contraintes sur la puissance totale de chaque centrale} $$ $$ N_{start,t}^{(X)} \leq N_t^{(X)} \leq N_{start,t}^{(X)}+N_{t-1}^{(X)} \text{ , Contraintes sur le nombre de centrales allumées possible} $$ $$ 0 \leq N_{start,t}^{(X)} \leq N^{(X)}-N_{t-1}^{(X)} \text{ , Contraintes sur le nombre de centrales démarrable possible} $$ $$ \sum_X P_t^{(X)} = D_t \text{ , Contrainte équilibre offre-demande} $$ Objectif : $$ \text{Minimiser} \sum_X \sum_T (P_t^{(X)} - P_{min}^{(X)}N_t^{(X)}) C_{MWh}^{(X)} + N_t^{(X)}C_{base}^{(X)} + N_{start,t}^{(X)}C_{start}^{(X)} $$
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 312 rows, 216 columns and 714 nonzeros
Model fingerprint: 0xafd71f6e
Variable types: 72 continuous, 144 integer (0 binary)
Coefficient statistics:
Matrix range [1e+00, 4e+03]
Objective range [1e+00, 2e+03]
Bounds range [5e+00, 1e+01]
RHS range [5e+00, 4e+04]
Found heuristic solution: objective 1474375.0000
Presolve removed 108 rows and 30 columns
Presolve time: 0.00s
Presolved: 204 rows, 186 columns, 522 nonzeros
Variable types: 42 continuous, 144 integer (0 binary)
Found heuristic solution: objective 1378930.0000
Root relaxation: objective 1.011257e+06, 52 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 1011257.14 0 26 1378930.00 1011257.14 26.7% - 0s
H 0 0 1019660.0000 1011257.14 0.82% - 0s
H 0 0 1018090.0000 1011257.14 0.67% - 0s
H 0 0 1016340.0000 1011257.14 0.50% - 0s
H 0 0 1016100.0000 1011257.14 0.48% - 0s
0 0 1014233.33 0 4 1016100.00 1014233.33 0.18% - 0s
H 0 0 1015860.0000 1014233.33 0.16% - 0s
H 0 0 1014650.0000 1014233.33 0.04% - 0s
H 0 0 1014400.0000 1014233.33 0.02% - 0s
Cutting planes:
Gomory: 3
MIR: 27
StrongCG: 2
Explored 1 nodes (92 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)
Solution count 9: 1.0144e+06 1.01465e+06 1.01586e+06 ... 1.47438e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 1.014400000000e+06, best bound 1.014400000000e+06, gap 0.0000%
Pour intégrer la réserve de puissance on ajoute la contrainte : $$ \sum_X N_t^{(X)}P_{max}^{(X)}\geq D_t\times 1,15 $$
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 336 rows, 216 columns and 786 nonzeros
Model fingerprint: 0x11b5f8ee
Variable types: 72 continuous, 144 integer (0 binary)
Coefficient statistics:
Matrix range [1e+00, 4e+03]
Objective range [1e+00, 2e+03]
Bounds range [5e+00, 1e+01]
RHS range [5e+00, 5e+04]
MIP start from previous solve did not produce a new incumbent solution
MIP start from previous solve violates constraint Réserve_de_puissance_à_15 by 4500.000000000
Found heuristic solution: objective 1316565.0000
Presolve removed 108 rows and 30 columns
Presolve time: 0.00s
Presolved: 228 rows, 186 columns, 594 nonzeros
Found heuristic solution: objective 1229165.0000
Variable types: 42 continuous, 144 integer (0 binary)
Found heuristic solution: objective 1198245.0000
Root relaxation: objective 1.012257e+06, 59 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 1012257.14 0 26 1198245.00 1012257.14 15.5% - 0s
H 0 0 1020660.0000 1012257.14 0.82% - 0s
H 0 0 1017340.0000 1012257.14 0.50% - 0s
H 0 0 1017100.0000 1012257.14 0.48% - 0s
0 0 1015150.00 0 12 1017100.00 1015150.00 0.19% - 0s
H 0 0 1016860.0000 1015150.00 0.17% - 0s
H 0 0 1015725.0000 1015150.00 0.06% - 0s
H 0 0 1015150.0000 1015150.00 0.00% - 0s
Cutting planes:
Gomory: 1
MIR: 25
Explored 1 nodes (94 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)
Solution count 9: 1.01515e+06 1.01572e+06 1.01686e+06 ... 1.31657e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 1.015150000000e+06, best bound 1.015150000000e+06, gap 0.0000%
Pour ce problème on modifie la convention $N_{-1}^{(X)}=0$ par $N_{-1}^{(X)}=N_{23}^{(X)}$
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 336 rows, 216 columns and 792 nonzeros
Model fingerprint: 0xfaf92924
Variable types: 72 continuous, 144 integer (0 binary)
Coefficient statistics:
Matrix range [1e+00, 4e+03]
Objective range [1e+00, 2e+03]
Bounds range [5e+00, 1e+01]
RHS range [5e+00, 5e+04]
Found heuristic solution: objective 1313700.0000
Presolve removed 105 rows and 27 columns
Presolve time: 0.00s
Presolved: 231 rows, 189 columns, 603 nonzeros
Found heuristic solution: objective 1225165.0000
Variable types: 42 continuous, 147 integer (0 binary)
Found heuristic solution: objective 1192195.0000
Root relaxation: objective 9.855143e+05, 54 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 985514.286 0 26 1192195.00 985514.286 17.3% - 0s
H 0 0 993725.00000 985514.286 0.83% - 0s
H 0 0 990405.00000 985514.286 0.49% - 0s
H 0 0 990165.00000 985514.286 0.47% - 0s
H 0 0 989030.00000 988540.000 0.05% - 0s
0 0 988540.000 0 3 989030.000 988540.000 0.05% - 0s
H 0 0 988540.00000 988540.000 0.00% - 0s
0 0 988540.000 0 3 988540.000 988540.000 0.00% - 0s
Cutting planes:
MIR: 18
Explored 1 nodes (85 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)
Solution count 8: 988540 989030 990165 ... 1.3137e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 9.885400000000e+05, best bound 9.885400000000e+05, gap 0.0000%
On ajoute les variables de décisions suivantes:
pour $Y\in[9,14]$ (pour les centrales de 900 MW et 1400MW),
$$
H_t^{(Y)} \in \{0,1\} \text{ , vaut 1 si la centrale $Y$ fonctionne à } t \text{ h 0 sinon}
$$
$$
H_{start,t}^{(Y)} \in \{0,1\} \text{ , vaut 1 si la centrale $Y$ démarre à } t \text{ h 0 sinon}
$$
Avec les contraintes :
$$
H_{start,t}^{(Y)} \leq 1 - H_{t-1}^{(Y)} \text{ , S'il y a un démarrage alors la centrale n'était pas allumée}
$$
Autre option :
$$
H_{t}^{(Y)} \leq H_{start,t}^{(Y)} + H_{t-1}^{(Y)} \text{ , Si la centrale fonctionne alors elle était allumée ou elle démarre}
$$
$$
H_{start,t}^{(Y)} \leq H_{t}^{(Y)} \text{ , La centrale fonctionne lorsqu'elle est est démarrée}
$$
$$
\sum_X P_t^{(X)} + \sum_Y N_t^{(Y)}P^{(Y)}= D_t \text{ , Contrainte équilibre offre-demande}
$$
$$
\sum_X N_t^{(X)}P_{max}^{(X)} + \sum_Y P^{(Y)}\geq D_t\times 1,15 \text{ , marges de sécurité}
$$
L'objectif mis à jour devient:
$$
\text{Minimiser} \sum_X \sum_t (P_t^{(X)} - P_{min}^{(X)}N_t^{(X)}) C_{MWh}^{(X)} + N_t^{(X)}C_{base}^{(X)} + N_{start,t}^{(X)}C_{start}^{(X)} + \sum_Y \sum_t H_t^{(Y)}C_{base}^{(Y)} + H_t^{(Y)}C_{start}^{(Y)}
$$
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 432 rows, 312 columns and 1080 nonzeros
Model fingerprint: 0x568b7ef7
Variable types: 72 continuous, 240 integer (96 binary)
Coefficient statistics:
Matrix range [1e+00, 4e+03]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+01]
RHS range [5e+00, 4e+04]
Found heuristic solution: objective 1447255.0000
Presolve removed 120 rows and 0 columns
Presolve time: 0.00s
Presolved: 312 rows, 312 columns, 840 nonzeros
Variable types: 72 continuous, 240 integer (96 binary)
Found heuristic solution: objective 1429430.0000
Root relaxation: objective 8.884163e+05, 90 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 888416.250 0 30 1429430.00 888416.250 37.8% - 0s
H 0 0 906941.25000 888416.250 2.04% - 0s
H 0 0 893135.00000 888416.250 0.53% - 0s
H 0 0 890510.00000 888416.250 0.24% - 0s
H 0 0 890260.00000 888474.286 0.20% - 0s
0 0 890176.667 0 22 890260.000 890176.667 0.01% - 0s
Cutting planes:
Gomory: 2
MIR: 33
Explored 1 nodes (132 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)
Solution count 6: 890260 890510 893135 ... 1.44726e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 8.902600000000e+05, best bound 8.901766666667e+05, gap 0.0094%
On ajoute les variables de décision suivante :
$$
S_t = \text{Puissance appelée par le pompage à l'instant }t
$$
Puis la contrainte :
$$
\sum_tS_t d^{(S)} = \sum_{t,Y} H_t^{(Y)}d^{(Y)}
$$
Où $d^{(S)}$ représente la hauteur d'eau élevée par MWh et $d^{(Y)}$ la hauteur d'eau prélevée lorsque la centrale $Y$ fonctionne.
On met à jour les contraintes suivante:
$$
\sum_X P_t^{(X)} + \sum_Y H_t^{(Y)}P^{(Y)}-S_t= D_t \text{ , Contrainte équilibre offre-demande}
$$
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 433 rows, 336 columns and 1176 nonzeros
Model fingerprint: 0x2bb1f118
Variable types: 96 continuous, 240 integer (96 binary)
Coefficient statistics:
Matrix range [3e-04, 4e+03]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+01]
RHS range [5e+00, 4e+04]
Found heuristic solution: objective 1468770.0000
Presolve removed 120 rows and 0 columns
Presolve time: 0.00s
Presolved: 313 rows, 336 columns, 936 nonzeros
Variable types: 96 continuous, 240 integer (96 binary)
Found heuristic solution: objective 1428970.0000
Root relaxation: objective 9.850143e+05, 145 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 985014.286 0 26 1428970.00 985014.286 31.1% - 0s
H 0 0 994935.00000 985014.286 1.00% - 0s
H 0 0 991890.00000 985014.286 0.69% - 0s
H 0 0 990145.00000 985014.286 0.52% - 0s
0 0 985814.126 0 48 990145.000 985814.126 0.44% - 0s
0 0 985814.126 0 48 990145.000 985814.126 0.44% - 0s
H 0 0 988290.00000 985814.126 0.25% - 0s
H 0 0 988040.00000 985814.126 0.23% - 0s
0 2 985814.126 0 48 988040.000 985814.126 0.23% - 0s
H 2 4 988002.00000 986022.114 0.20% 4.0 0s
H 5 8 986630.00000 986022.114 0.06% 8.8 0s
H 21 13 986290.00000 986051.521 0.02% 8.0 0s
Cutting planes:
Gomory: 5
MIR: 24
Explored 45 nodes (439 simplex iterations) in 0.10 seconds (0.04 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 986290 986630 988002 ... 1.46877e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 9.862900000000e+05, best bound 9.862900000000e+05, gap 0.0000%
Les variables de décisions concernant l'hydroélectricité deviennent : $$ H_t^{(Y,n)} \in \{0,1\} = \text{La centrale hydroélectrique } Y \text{ fonctionne au palier } n \text{ à l'instant } t $$ $$ H_{start,t}^{(Y)} \in \{0,1\} = \text{ La centrale hydroélectrique $Y$ démarre à l'instant $t$} $$ Les contraintes suivantes sont modifiées :
$$ \text{Equilibre offre-demande : } \sum_X P_t^{(X)} + \sum_{Y,n} H_t^{(Y,n)}P^{(Y,n)}-S_t= D_t $$$$ \text{Réserve de puissance : } \sum_X N_t^{(X)}P_{max}^{(X)} + \sum_Y P^{(Y,n_{max})}\geq D_t\times 1,15 $$$$ \text{Niveau réservoir : } \sum_t S_t d^{(S)} = \sum_{t,Y,n} H_t^{(Y,n)}d^{(Y,n)} $$Les contraintes sur les démarrages et les paliers deviennent : $$ \text{Un seul palier fonctionne à la fois , }\sum_n H_t^{(Y,n)} \leq 1 $$ $$ \text{ Si un palier fonctionne alors il y avait déjà un palier actif ou la centrale est démarrée , } H_t^{(Y,n)} \leq \sum_n H_{t-1}^{(Y,n)} + H_{start,t}^{(Y)} $$ Modification de la fonction objectif : $$ \text{Minimiser} \sum_X \sum_t (P_t^{(X)} - P_{min}^{(X)}N_t^{(X)}) C_{MWh}^{(X)} + N_t^{(X)}C_{base}^{(X)} + N_{start,t}^{(X)}C_{start}^{(X)} + \sum_{Y,n} \sum_t H_t^{(Y,n)}C_{base}^{(Y,n)} + \sum_Y H_{start,t}^{(Y)}C_{start}^{(Y)} $$ Où $P^{(Y,n)}$ est la puissance de la centrale $Y$ au palier $n$, $d^{(Y,n)}$ est l'abaissement sur une heure quand la centrale $Y$ fonctionne au palier $n$ et $C_{base}^{(Y,n)}$ est le coût du fonctionnement de la centrale $Y$ pendant une heure de fonctionnement au palier $n$
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 577 rows, 480 columns and 3144 nonzeros
Model fingerprint: 0x0ee78a89
Variable types: 96 continuous, 384 integer (240 binary)
Coefficient statistics:
Matrix range [3e-04, 4e+03]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+01]
RHS range [1e+00, 4e+04]
Presolve removed 216 rows and 0 columns
Presolve time: 0.00s
Presolved: 361 rows, 480 columns, 1704 nonzeros
Variable types: 96 continuous, 384 integer (240 binary)
Found heuristic solution: objective 1114770.0000
Found heuristic solution: objective 1086990.0000
Found heuristic solution: objective 1026475.0000
Root relaxation: objective 9.850143e+05, 244 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 985014.286 0 26 1026475.00 985014.286 4.04% - 0s
H 0 0 994935.00000 985014.286 1.00% - 0s
H 0 0 990145.00000 985014.286 0.52% - 0s
H 0 0 987635.00000 985677.273 0.20% - 0s
0 0 985677.273 0 48 987635.000 985677.273 0.20% - 0s
H 0 0 987176.00000 985677.273 0.15% - 0s
0 0 985681.649 0 48 987176.000 985681.649 0.15% - 0s
0 0 985681.649 0 26 987176.000 985681.649 0.15% - 0s
0 0 985681.649 0 48 987176.000 985681.649 0.15% - 0s
H 0 0 987076.00000 985681.649 0.14% - 0s
0 0 985687.391 0 48 987076.000 985687.391 0.14% - 0s
H 0 0 986256.00000 985687.391 0.06% - 0s
0 0 985687.391 0 21 986256.000 985687.391 0.06% - 0s
0 0 985687.391 0 45 986256.000 985687.391 0.06% - 0s
0 0 985687.391 0 41 986256.000 985687.391 0.06% - 0s
0 0 985687.391 0 41 986256.000 985687.391 0.06% - 0s
0 2 985687.391 0 41 986256.000 985687.391 0.06% - 0s
H 28 7 986160.00000 985789.464 0.04% 9.4 0s
Cutting planes:
Gomory: 2
MIR: 22
Explored 50 nodes (1170 simplex iterations) in 0.21 seconds (0.07 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 986160 986256 987076 ... 1.11477e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 9.861600000000e+05, best bound 9.861380000000e+05, gap 0.0022%
On introduit la variable de décision suivante : $$ N^{S}_t \in \{0,1\} = \text{La pompage est en fonctionnement} $$ On ajoute les contraintes suivante : $$ \text{Si une centrale hydroélectrique est activée alors le pompage est désactivé , } \frac{1}{\text{Nb centrale hydro}}\sum_{Y,n}H_t^{Y,n} \leq 1 - N_t^{(S)} $$ $$ \text{Si aucune centrale hydroélectrique est allumée alors il peut y avoir du pompage , } S_t \leq M \times N_t^{(S)} $$
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 625 rows, 504 columns and 3408 nonzeros
Model fingerprint: 0xa2175415
Variable types: 96 continuous, 408 integer (264 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+01]
RHS range [1e+00, 4e+04]
Presolve removed 240 rows and 0 columns
Presolve time: 0.01s
Presolved: 385 rows, 504 columns, 1800 nonzeros
Variable types: 96 continuous, 408 integer (264 binary)
Found heuristic solution: objective 1155935.0000
Found heuristic solution: objective 1086990.0000
Found heuristic solution: objective 1029100.0000
Root relaxation: objective 9.850143e+05, 210 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 985014.286 0 26 1029100.00 985014.286 4.28% - 0s
H 0 0 994935.00000 985014.286 1.00% - 0s
H 0 0 990145.00000 985014.286 0.52% - 0s
H 0 0 989730.00000 985677.273 0.41% - 0s
0 0 985677.273 0 66 989730.000 985677.273 0.41% - 0s
0 0 985692.849 0 72 989730.000 985692.849 0.41% - 0s
H 0 0 988290.00000 985692.849 0.26% - 0s
0 0 985697.389 0 72 988290.000 985697.389 0.26% - 0s
H 0 0 988040.00000 985697.389 0.24% - 0s
0 2 985697.389 0 72 988040.000 985697.389 0.24% - 0s
H 35 40 986855.00000 986007.287 0.09% 16.7 0s
H 75 56 986771.00000 986031.356 0.07% 13.3 0s
Cutting planes:
MIR: 54
Explored 335 nodes (4215 simplex iterations) in 0.21 seconds (0.14 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 986771 986771 986855 ... 1.08699e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 9.867710000000e+05, best bound 9.866744586729e+05, gap 0.0098%
Variables de décision : Pour une type de centrale $X \in [A,B,C]$, $k$ l'identification de la $k$-ieme centrale, et une heure de la journée $t\in {1,\dots,24}$, on définit : $$ N_t^{(X,k)} \in\{0,1\} \text{La $k$-ieme centrale $X$ fonctionne à $t$} $$ $$ N_{start,t}^{(X,k)} \in\{0,1\} \text{La $k$-ieme centrale $X$ est démarrée à $t$} $$ $$ P_t^{(X,k)} = \text{Puissance de la $k$-ième centrale $X$ à l'instant $t$} $$ Contraintes : $$ N_t^{(X,k)} P_{min}^{(X)} \leq P_t^{(X,k)} \leq N_t^{(X,k)} P_{max}^{(X)} \text{ , Contraintes sur la puissance totale de chaque centrale} $$ $$ \text{Equilibre offre-demande : } \sum_X \sum_{k=1}^{N^{(X)}} P_t^{(X,k)} + \sum_{Y,n} H_t^{(Y,n)}P^{(Y,n)}-S_t= D_t $$ $$ \text{Réserve de puissance : } \sum_X \sum_{k=1}^{N^{(X)}} N_t^{(X,k)}P_{max}^{(X)} + \sum_Y P^{(Y,n_{max})}\geq D_t\times 1,15 $$ Objectif : $$ \text{Minimiser} \sum_X \sum_{k=1}^{N^{(X)}} \sum_t (P_t^{(X,k)} - P_{min}^{(X)}N_t^{(X,k)}) C_{MWh}^{(X)} + N_t^{(X,k)}C_{base}^{(X)} + N_{start,t}^{(X,k)}C_{start}^{(X)} + \sum_{Y,n} \sum_t H_t^{(Y,n)}C_{base}^{(Y,n)} + \sum_Y H_{start,t}^{(Y)}C_{start}^{(Y)} $$
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 2281 rows, 2232 columns and 8448 nonzeros
Model fingerprint: 0x68b994eb
Variable types: 672 continuous, 1560 integer (1560 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 4e+04]
Presolve removed 168 rows and 0 columns
Presolve time: 0.01s
Presolved: 2113 rows, 2232 columns, 6984 nonzeros
Variable types: 672 continuous, 1560 integer (1560 binary)
Found heuristic solution: objective 1066070.0000
Found heuristic solution: objective 1049400.0000
Found heuristic solution: objective 1031950.0000
Root relaxation: objective 9.848205e+05, 1445 iterations, 0.02 seconds (0.01 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 984820.536 0 31 1031950.00 984820.536 4.57% - 0s
H 0 0 990145.00000 984820.536 0.54% - 0s
H 0 0 989980.00000 985527.783 0.45% - 0s
0 0 985527.783 0 75 989980.000 985527.783 0.45% - 0s
H 0 0 989730.00000 985527.783 0.42% - 0s
0 0 985527.783 0 75 989730.000 985527.783 0.42% - 0s
0 0 985550.204 0 98 989730.000 985550.204 0.42% - 0s
0 0 985550.204 0 98 989730.000 985550.204 0.42% - 0s
H 0 0 988837.00000 985550.204 0.33% - 0s
0 0 985680.000 0 100 988837.000 985680.000 0.32% - 0s
H 0 0 988697.00000 985680.000 0.31% - 0s
0 0 985680.000 0 105 988697.000 985680.000 0.31% - 0s
0 0 985680.000 0 94 988697.000 985680.000 0.31% - 0s
0 0 985680.000 0 73 988697.000 985680.000 0.31% - 0s
0 0 985680.000 0 73 988697.000 985680.000 0.31% - 0s
0 0 985680.000 0 73 988697.000 985680.000 0.31% - 0s
H 0 0 987354.00000 985680.000 0.17% - 0s
0 0 985680.000 0 28 987354.000 985680.000 0.17% - 0s
0 0 985680.000 0 68 987354.000 985680.000 0.17% - 0s
0 0 985680.000 0 80 987354.000 985680.000 0.17% - 0s
0 0 985681.190 0 102 987354.000 985681.190 0.17% - 0s
0 0 985681.190 0 102 987354.000 985681.190 0.17% - 0s
0 0 985681.548 0 101 987354.000 985681.548 0.17% - 0s
0 0 985681.548 0 80 987354.000 985681.548 0.17% - 0s
H 0 0 987114.00000 985681.548 0.15% - 0s
0 2 985681.548 0 79 987114.000 985681.548 0.15% - 0s
H 289 189 986827.00000 986050.750 0.08% 12.7 1s
H 343 220 986818.00000 986165.714 0.07% 12.6 1s
H 431 223 986817.99949 986165.714 0.07% 11.7 1s
* 6256 389 39 986775.00000 986657.391 0.01% 9.0 2s
Cutting planes:
Cover: 15
Implied bound: 3
MIR: 32
Flow cover: 43
GUB cover: 3
Inf proof: 2
RLT: 6
Relax-and-lift: 1
Explored 7129 nodes (66927 simplex iterations) in 3.11 seconds (3.66 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 986775 986818 986827 ... 989730
Optimal solution found (tolerance 1.00e-04)
Best objective 9.867750000000e+05, best bound 9.867288756614e+05, gap 0.0047%
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 2281 rows, 2232 columns and 8448 nonzeros
Model fingerprint: 0x65e31120
Variable types: 672 continuous, 1560 integer (1560 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 5e+04]
Presolve removed 168 rows and 0 columns
Presolve time: 0.01s
Presolved: 2113 rows, 2232 columns, 6984 nonzeros
Variable types: 672 continuous, 1560 integer (1560 binary)
Found heuristic solution: objective 1070205.0000
Found heuristic solution: objective 1068650.0000
Root relaxation: objective 9.865919e+05, 1422 iterations, 0.01 seconds (0.01 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 986591.867 0 57 1068650.00 986591.867 7.68% - 0s
H 0 0 1001855.0000 986591.867 1.52% - 0s
H 0 0 999480.00000 986591.867 1.29% - 0s
H 0 0 992900.00000 986591.867 0.64% - 0s
0 0 986628.571 0 100 992900.000 986628.571 0.63% - 0s
0 0 986659.053 0 93 992900.000 986659.053 0.63% - 0s
0 0 986748.434 0 91 992900.000 986748.434 0.62% - 0s
0 0 986757.183 0 100 992900.000 986757.183 0.62% - 0s
0 0 986757.183 0 109 992900.000 986757.183 0.62% - 0s
H 0 0 990449.00000 986757.183 0.37% - 0s
0 0 986805.247 0 102 990449.000 986805.247 0.37% - 0s
H 0 0 989007.00000 986822.410 0.22% - 0s
0 0 986822.410 0 79 989007.000 986822.410 0.22% - 0s
0 0 986824.328 0 89 989007.000 986824.328 0.22% - 0s
0 0 986824.328 0 114 989007.000 986824.328 0.22% - 0s
H 0 0 988370.00000 986824.328 0.16% - 0s
H 0 0 988365.00000 986824.328 0.16% - 0s
0 0 986828.816 0 123 988365.000 986828.816 0.16% - 0s
0 0 986828.816 0 56 988365.000 986828.816 0.16% - 0s
0 0 986828.816 0 108 988365.000 986828.816 0.16% - 0s
0 0 986828.816 0 96 988365.000 986828.816 0.16% - 0s
0 0 986828.816 0 114 988365.000 986828.816 0.16% - 0s
0 0 986828.816 0 161 988365.000 986828.816 0.16% - 0s
0 0 986840.551 0 133 988365.000 986840.551 0.15% - 0s
0 0 986841.262 0 133 988365.000 986841.262 0.15% - 0s
0 0 986860.211 0 155 988365.000 986860.211 0.15% - 0s
0 0 986879.786 0 163 988365.000 986879.786 0.15% - 0s
0 0 986882.243 0 168 988365.000 986882.243 0.15% - 0s
0 0 986882.328 0 167 988365.000 986882.328 0.15% - 0s
0 0 986910.332 0 142 988365.000 986910.332 0.15% - 0s
0 0 986922.008 0 130 988365.000 986922.008 0.15% - 0s
0 0 986928.169 0 134 988365.000 986928.169 0.15% - 0s
0 0 986928.169 0 143 988365.000 986928.169 0.15% - 0s
0 0 986930.642 0 158 988365.000 986930.642 0.15% - 0s
0 0 986930.642 0 127 988365.000 986930.642 0.15% - 0s
H 0 0 988235.00000 986930.642 0.13% - 0s
0 2 986930.642 0 116 988235.000 986930.642 0.13% - 0s
H 35 39 988040.00000 987410.256 0.06% 14.9 0s
H 80 82 988035.00000 987410.256 0.06% 12.2 0s
H 89 82 988015.00000 987410.256 0.06% 11.6 0s
H 152 140 987767.00000 987441.255 0.03% 10.3 0s
H 169 140 987762.00000 987441.255 0.03% 10.0 0s
H 268 220 987760.00000 987450.150 0.03% 8.7 1s
H 288 220 987620.00000 987450.150 0.02% 8.9 1s
H 355 253 987615.00000 987450.629 0.02% 9.7 1s
Cutting planes:
Gomory: 3
Implied bound: 5
Projected implied bound: 1
MIR: 11
StrongCG: 1
Flow cover: 12
Relax-and-lift: 2
Explored 2469 nodes (24742 simplex iterations) in 2.67 seconds (1.73 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 987615 987615 987615 ... 988015
Optimal solution found (tolerance 1.00e-04)
Best objective 9.876150000000e+05, best bound 9.875199699458e+05, gap 0.0096%
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 2281 rows, 2232 columns and 8448 nonzeros
Model fingerprint: 0x9893fba4
Variable types: 672 continuous, 1560 integer (1560 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 4e+04]
Presolve removed 168 rows and 0 columns
Presolve time: 0.01s
Presolved: 2113 rows, 2232 columns, 6984 nonzeros
Variable types: 672 continuous, 1560 integer (1560 binary)
Found heuristic solution: objective 1065810.0000
Found heuristic solution: objective 1049600.0000
Root relaxation: objective 9.892817e+05, 1484 iterations, 0.01 seconds (0.02 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 989281.715 0 54 1049600.00 989281.715 5.75% - 0s
H 0 0 1008655.0000 989281.715 1.92% - 0s
H 0 0 1003320.0000 989281.715 1.40% - 0s
H 0 0 991750.00000 989281.715 0.25% - 0s
0 0 989568.409 0 49 991750.000 989568.409 0.22% - 0s
0 0 989568.409 0 49 991750.000 989568.409 0.22% - 0s
H 0 0 990860.00000 989568.409 0.13% - 0s
0 0 989583.635 0 54 990860.000 989583.635 0.13% - 0s
0 0 989583.635 0 54 990860.000 989583.635 0.13% - 0s
H 0 0 990500.00000 989583.635 0.09% - 0s
0 0 989583.635 0 60 990500.000 989583.635 0.09% - 0s
0 0 989594.782 0 68 990500.000 989594.782 0.09% - 0s
0 0 989609.740 0 79 990500.000 989609.740 0.09% - 0s
0 0 989609.978 0 81 990500.000 989609.978 0.09% - 0s
0 0 989733.996 0 86 990500.000 989733.996 0.08% - 0s
0 0 989733.996 0 60 990500.000 989733.996 0.08% - 0s
0 0 989734.282 0 92 990500.000 989734.282 0.08% - 0s
0 0 989734.807 0 95 990500.000 989734.807 0.08% - 0s
0 0 989734.807 0 95 990500.000 989734.807 0.08% - 0s
0 0 989734.807 0 101 990500.000 989734.807 0.08% - 0s
0 0 989734.807 0 93 990500.000 989734.807 0.08% - 0s
H 0 0 990440.00000 989734.807 0.07% - 0s
0 0 989734.807 0 42 990440.000 989734.807 0.07% - 0s
0 0 989734.807 0 47 990440.000 989734.807 0.07% - 0s
0 0 989757.223 0 43 990440.000 989757.223 0.07% - 0s
0 0 989757.714 0 56 990440.000 989757.714 0.07% - 0s
0 0 989757.714 0 76 990440.000 989757.714 0.07% - 0s
0 0 989757.987 0 75 990440.000 989757.987 0.07% - 0s
0 0 989758.118 0 75 990440.000 989758.118 0.07% - 0s
0 0 989758.118 0 89 990440.000 989758.118 0.07% - 0s
0 0 989758.118 0 89 990440.000 989758.118 0.07% - 0s
0 0 989763.110 0 49 990440.000 989763.110 0.07% - 0s
0 0 989763.199 0 41 990440.000 989763.199 0.07% - 0s
0 0 989778.249 0 41 990440.000 989778.249 0.07% - 0s
0 0 989897.866 0 28 990440.000 989897.866 0.05% - 0s
0 0 989897.866 0 28 990440.000 989897.866 0.05% - 0s
0 2 989897.866 0 28 990440.000 989897.866 0.05% - 0s
* 434 281 46 990430.00000 990122.540 0.03% 5.3 1s
H 979 626 990420.00000 990122.540 0.03% 5.3 1s
H 1701 719 990410.00000 990122.540 0.03% 6.1 1s
Cutting planes:
Gomory: 9
Lift-and-project: 1
MIR: 79
Flow cover: 53
RLT: 2
Explored 26619 nodes (185253 simplex iterations) in 4.81 seconds (3.82 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 990410 990420 990430 ... 991750
Optimal solution found (tolerance 1.00e-04)
Best objective 9.904100000000e+05, best bound 9.903183333333e+05, gap 0.0093%
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 2294 rows, 2232 columns and 8604 nonzeros
Model fingerprint: 0xcd2d20ff
Variable types: 672 continuous, 1560 integer (1560 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 4e+04]
Presolve removed 168 rows and 0 columns
Presolve time: 0.02s
Presolved: 2126 rows, 2232 columns, 7140 nonzeros
Variable types: 672 continuous, 1560 integer (1560 binary)
Found heuristic solution: objective 1047065.0000
Found heuristic solution: objective 1045750.0000
Root relaxation: objective 1.003420e+06, 1703 iterations, 0.02 seconds (0.02 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 1003419.59 0 51 1045750.00 1003419.59 4.05% - 0s
H 0 0 1025155.0000 1003419.59 2.12% - 0s
H 0 0 1012530.0000 1003419.59 0.90% - 0s
0 0 1003700.84 0 91 1012530.00 1003700.84 0.87% - 0s
H 0 0 1011550.0000 1003700.84 0.78% - 0s
H 0 0 1011486.0000 1003700.84 0.77% - 0s
0 0 1003702.54 0 113 1011486.00 1003702.54 0.77% - 0s
0 0 1003702.54 0 120 1011486.00 1003702.54 0.77% - 0s
0 0 1003815.55 0 87 1011486.00 1003815.55 0.76% - 0s
0 0 1003906.43 0 59 1011486.00 1003906.43 0.75% - 0s
H 0 0 1008770.0000 1003906.43 0.48% - 0s
0 0 1004239.12 0 121 1008770.00 1004239.12 0.45% - 0s
0 0 1004239.12 0 122 1008770.00 1004239.12 0.45% - 0s
0 0 1004289.66 0 95 1008770.00 1004289.66 0.44% - 0s
0 0 1004289.66 0 111 1008770.00 1004289.66 0.44% - 0s
0 0 1004289.66 0 88 1008770.00 1004289.66 0.44% - 0s
0 0 1004289.66 0 99 1008770.00 1004289.66 0.44% - 0s
0 0 1004289.66 0 72 1008770.00 1004289.66 0.44% - 0s
0 0 1004289.66 0 107 1008770.00 1004289.66 0.44% - 0s
0 0 1004289.66 0 96 1008770.00 1004289.66 0.44% - 0s
0 0 1004289.66 0 75 1008770.00 1004289.66 0.44% - 0s
H 0 0 1006700.0000 1004289.66 0.24% - 0s
0 2 1004289.66 0 75 1006700.00 1004289.66 0.24% - 0s
H 71 77 1006622.0000 1004528.51 0.21% 15.2 0s
H 112 121 1006305.0000 1004528.51 0.18% 12.6 0s
H 170 166 1005559.0000 1004528.51 0.10% 10.8 0s
H 293 290 1005405.0000 1004539.36 0.09% 9.2 1s
* 939 571 38 1005395.0000 1004565.24 0.08% 8.8 1s
H 1196 607 1005350.0000 1004761.71 0.06% 5.0 4s
* 1313 608 45 1005300.0000 1004767.86 0.05% 5.2 4s
4532 1299 1005184.17 41 31 1005300.00 1004783.47 0.05% 6.9 5s
28672 3865 1005157.28 48 42 1005300.00 1005058.89 0.02% 8.5 10s
Cutting planes:
Gomory: 36
Implied bound: 1
MIR: 31
Flow cover: 22
Explored 35957 nodes (310944 simplex iterations) in 11.28 seconds (10.07 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 1.0053e+06 1.0053e+06 1.00535e+06 ... 1.00877e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 1.005300000000e+06, best bound 1.005206348214e+06, gap 0.0093%
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 2929 rows, 2232 columns and 9744 nonzeros
Model fingerprint: 0xfe91f2fc
Variable types: 672 continuous, 1560 integer (1560 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 4e+04]
Presolve removed 839 rows and 1269 columns
Presolve time: 0.02s
Presolved: 2090 rows, 963 columns, 6363 nonzeros
Variable types: 672 continuous, 291 integer (291 binary)
Root relaxation: objective 1.011158e+06, 1035 iterations, 0.01 seconds (0.01 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 1011158.36 0 42 - 1011158.36 - - 0s
H 0 0 1024447.0000 1011158.36 1.30% - 0s
0 0 1011766.70 0 37 1024447.00 1011766.70 1.24% - 0s
0 0 1012487.81 0 17 1024447.00 1012487.81 1.17% - 0s
0 0 1012487.81 0 17 1024447.00 1012487.81 1.17% - 0s
H 0 0 1019980.0000 1012487.81 0.73% - 0s
0 0 1012528.31 0 18 1019980.00 1012528.31 0.73% - 0s
0 0 1012528.31 0 18 1019980.00 1012528.31 0.73% - 0s
0 0 1012528.31 0 19 1019980.00 1012528.31 0.73% - 0s
0 0 1012528.31 0 18 1019980.00 1012528.31 0.73% - 0s
0 0 1012637.32 0 19 1019980.00 1012637.32 0.72% - 0s
0 0 1012637.32 0 17 1019980.00 1012637.32 0.72% - 0s
H 0 0 1017238.0000 1012637.32 0.45% - 0s
0 0 1012637.32 0 19 1017238.00 1012637.32 0.45% - 0s
0 0 1012637.32 0 17 1017238.00 1012637.32 0.45% - 0s
H 0 0 1017184.0000 1012637.32 0.45% - 0s
0 0 1012637.32 0 18 1017184.00 1012637.32 0.45% - 0s
0 0 1012637.32 0 18 1017184.00 1012637.32 0.45% - 0s
0 0 1012637.32 0 20 1017184.00 1012637.32 0.45% - 0s
0 0 1012637.32 0 20 1017184.00 1012637.32 0.45% - 0s
H 0 0 1016994.0000 1012637.32 0.43% - 0s
0 0 1012637.32 0 17 1016994.00 1012637.32 0.43% - 0s
0 2 1012637.32 0 17 1016994.00 1012637.32 0.43% - 0s
H 27 3 1016430.0000 1015144.08 0.13% 16.0 0s
Cutting planes:
Gomory: 3
MIR: 17
Flow cover: 3
RLT: 7
Explored 49 nodes (2033 simplex iterations) in 0.52 seconds (0.28 work units)
Thread count was 8 (of 8 available processors)
Solution count 7: 1.01643e+06 1.01643e+06 1.01699e+06 ... 1.02445e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 1.016430000000e+06, best bound 1.016409639706e+06, gap 0.0020%
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 2929 rows, 2232 columns and 10392 nonzeros
Model fingerprint: 0x7fd3415b
Variable types: 672 continuous, 1560 integer (1560 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 4e+04]
Presolve removed 168 rows and 0 columns
Presolve time: 0.02s
Presolved: 2761 rows, 2232 columns, 9576 nonzeros
Variable types: 672 continuous, 1560 integer (1560 binary)
Found heuristic solution: objective 1143740.0000
Root relaxation: objective 9.865633e+05, 1541 iterations, 0.02 seconds (0.02 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 986563.290 0 133 1143740.00 986563.290 13.7% - 0s
H 0 0 1052540.0000 986563.290 6.27% - 0s
H 0 0 999785.00000 986563.290 1.32% - 0s
H 0 0 994685.00000 987113.421 0.76% - 0s
0 0 987113.421 0 126 994685.000 987113.421 0.76% - 0s
0 0 987306.646 0 120 994685.000 987306.646 0.74% - 0s
0 0 987886.769 0 121 994685.000 987886.769 0.68% - 0s
0 0 987887.226 0 122 994685.000 987887.226 0.68% - 0s
0 0 988302.092 0 135 994685.000 988302.092 0.64% - 0s
0 0 988304.690 0 140 994685.000 988304.690 0.64% - 0s
0 0 988309.044 0 152 994685.000 988309.044 0.64% - 0s
0 0 988309.044 0 152 994685.000 988309.044 0.64% - 0s
0 0 988336.401 0 113 994685.000 988336.401 0.64% - 0s
0 0 988343.477 0 123 994685.000 988343.477 0.64% - 0s
0 0 988345.222 0 123 994685.000 988345.222 0.64% - 0s
H 0 0 994500.00000 988351.317 0.62% - 0s
0 0 988351.317 0 124 994500.000 988351.317 0.62% - 0s
0 0 988355.092 0 135 994500.000 988355.092 0.62% - 0s
H 0 0 992340.00000 988355.092 0.40% - 0s
H 0 0 992270.00000 988355.092 0.39% - 0s
0 0 988361.795 0 111 992270.000 988361.795 0.39% - 0s
0 0 988361.907 0 112 992270.000 988361.907 0.39% - 0s
0 0 988374.433 0 125 992270.000 988374.433 0.39% - 0s
0 0 988374.740 0 120 992270.000 988374.740 0.39% - 0s
0 0 988375.536 0 142 992270.000 988375.536 0.39% - 0s
0 0 988375.800 0 146 992270.000 988375.800 0.39% - 0s
0 0 988375.905 0 146 992270.000 988375.905 0.39% - 0s
0 0 988375.905 0 95 992270.000 988375.905 0.39% - 0s
0 2 988375.905 0 94 992270.000 988375.905 0.39% - 0s
H 31 40 991247.00000 988715.567 0.26% 32.8 0s
H 33 40 990205.00000 988715.567 0.15% 36.4 0s
H 78 74 989795.00000 988715.567 0.11% 24.3 1s
* 188 129 43 989790.00000 988751.375 0.10% 18.6 1s
H 396 240 989718.00000 988871.073 0.09% 16.4 1s
H 407 240 989660.00000 988871.073 0.08% 16.1 1s
H 417 240 989575.00000 988871.073 0.07% 16.0 1s
* 1017 490 53 989570.00000 988906.114 0.07% 12.7 1s
H 1201 513 989565.00000 988929.986 0.06% 15.3 3s
* 1601 580 50 989425.00000 988957.672 0.05% 13.9 3s
* 1841 574 56 989415.00000 989028.615 0.04% 13.2 3s
* 2626 660 55 989352.00000 989102.739 0.03% 11.6 4s
* 2910 760 58 989350.00000 989113.997 0.02% 11.1 4s
5902 1694 cutoff 53 989350.000 989181.643 0.02% 8.7 5s
Cutting planes:
Gomory: 28
Implied bound: 33
MIR: 58
Flow cover: 37
Network: 1
RLT: 8
Relax-and-lift: 7
Explored 16360 nodes (126707 simplex iterations) in 7.60 seconds (6.30 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 989350 989352 989415 ... 989790
Optimal solution found (tolerance 1.00e-04)
Best objective 9.893500000000e+05, best bound 9.892542062638e+05, gap 0.0097%
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 3577 rows, 2232 columns and 13632 nonzeros
Model fingerprint: 0xf96e20e4
Variable types: 672 continuous, 1560 integer (1560 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 4e+04]
Presolve removed 168 rows and 0 columns
Presolve time: 0.02s
Presolved: 3409 rows, 2232 columns, 12168 nonzeros
Variable types: 672 continuous, 1560 integer (1560 binary)
Root relaxation: objective 9.870197e+05, 1824 iterations, 0.03 seconds (0.03 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 987019.698 0 120 - 987019.698 - - 0s
H 0 0 1006722.0000 987019.698 1.96% - 0s
H 0 0 997562.00000 987019.698 1.06% - 0s
H 0 0 993270.00000 987019.698 0.63% - 0s
0 0 987417.844 0 141 993270.000 987417.844 0.59% - 0s
0 0 987539.149 0 142 993270.000 987539.149 0.58% - 0s
0 0 988614.725 0 163 993270.000 988614.725 0.47% - 0s
0 0 988875.471 0 172 993270.000 988875.471 0.44% - 0s
0 0 988892.108 0 134 993270.000 988892.108 0.44% - 0s
0 0 988893.176 0 140 993270.000 988893.176 0.44% - 0s
0 0 988893.176 0 140 993270.000 988893.176 0.44% - 0s
0 0 989269.307 0 197 993270.000 989269.307 0.40% - 0s
0 0 989274.817 0 173 993270.000 989274.817 0.40% - 0s
0 0 989275.150 0 180 993270.000 989275.150 0.40% - 0s
0 0 989284.627 0 194 993270.000 989284.627 0.40% - 0s
0 0 989285.754 0 206 993270.000 989285.754 0.40% - 0s
0 0 989287.369 0 201 993270.000 989287.369 0.40% - 0s
0 0 989290.155 0 231 993270.000 989290.155 0.40% - 0s
0 0 989291.326 0 229 993270.000 989291.326 0.40% - 0s
0 0 989292.122 0 211 993270.000 989292.122 0.40% - 0s
0 0 989292.188 0 212 993270.000 989292.188 0.40% - 0s
0 0 989296.378 0 242 993270.000 989296.378 0.40% - 0s
0 0 989297.973 0 255 993270.000 989297.973 0.40% - 0s
0 0 989298.240 0 280 993270.000 989298.240 0.40% - 0s
0 0 989302.239 0 277 993270.000 989302.239 0.40% - 0s
0 0 989302.639 0 234 993270.000 989302.639 0.40% - 0s
0 0 989302.789 0 272 993270.000 989302.789 0.40% - 0s
0 0 989302.789 0 256 993270.000 989302.789 0.40% - 0s
H 0 0 993125.00000 989302.789 0.38% - 0s
0 2 989302.789 0 243 993125.000 989302.789 0.38% - 1s
H 161 100 992915.00000 989305.457 0.36% 39.2 1s
H 180 115 992805.00000 989308.155 0.35% 41.1 1s
H 290 169 992340.00000 989308.524 0.31% 39.9 1s
H 301 183 991085.00000 989309.688 0.18% 39.4 2s
H 332 191 991070.00000 989312.678 0.18% 38.7 2s
H 335 191 991030.00000 989312.678 0.17% 39.1 2s
* 616 301 70 990980.00000 989401.678 0.16% 31.1 2s
H 1078 510 990955.00000 989469.138 0.15% 25.8 4s
1080 512 990459.387 27 259 990955.000 989471.141 0.15% 25.8 5s
H 1272 580 990945.00000 989573.094 0.14% 30.9 6s
H 1276 553 990865.00000 989573.094 0.13% 30.8 6s
H 2990 1195 990855.00000 990219.079 0.06% 26.6 8s
H 3333 1372 990840.00000 990219.079 0.06% 25.8 8s
H 3366 1316 990810.00000 990219.079 0.06% 25.7 8s
4638 2098 990512.720 49 45 990810.000 990276.833 0.05% 25.6 10s
H 5197 2298 990800.00000 990289.607 0.05% 25.8 10s
* 6821 3103 61 990780.00000 990319.343 0.05% 25.7 11s
9576 4525 990411.262 40 146 990780.000 990342.643 0.04% 25.9 15s
14637 5938 990539.690 43 256 990780.000 990384.653 0.04% 26.7 21s
15031 6119 990496.749 62 52 990780.000 990384.653 0.04% 27.1 25s
H20428 7467 990779.99985 990395.841 0.04% 24.3 28s
24214 8548 cutoff 56 990780.000 990412.306 0.04% 23.4 30s
34489 9625 990456.741 60 178 990780.000 990445.638 0.03% 23.3 35s
43601 11997 990694.058 60 38 990780.000 990468.484 0.03% 23.9 40s
44666 12242 990725.859 69 64 990780.000 990470.746 0.03% 23.9 47s
49088 13265 cutoff 67 990780.000 990481.212 0.03% 24.2 50s
56959 14829 cutoff 72 990780.000 990497.310 0.03% 24.4 55s
65482 16194 990539.768 71 83 990780.000 990511.757 0.03% 24.6 60s
73506 17311 990659.188 67 98 990780.000 990525.493 0.03% 24.7 65s
81598 18172 990571.236 58 90 990780.000 990539.352 0.02% 24.8 70s
89096 18802 990688.666 66 34 990780.000 990551.142 0.02% 24.8 75s
97305 19225 990733.218 71 34 990780.000 990562.343 0.02% 25.0 80s
104548 19604 cutoff 67 990780.000 990570.983 0.02% 25.0 85s
111609 19603 cutoff 75 990780.000 990581.714 0.02% 25.1 90s
118951 19261 990769.142 70 111 990780.000 990592.531 0.02% 25.1 95s
123952 18823 cutoff 65 990780.000 990600.430 0.02% 25.1 100s
131922 18217 990667.143 66 80 990780.000 990612.646 0.02% 25.1 105s
138337 17488 990756.424 68 35 990780.000 990622.826 0.02% 25.0 110s
144125 16623 990655.970 76 109 990780.000 990631.592 0.01% 25.0 115s
150752 15761 990648.961 67 22 990780.000 990642.660 0.01% 24.9 120s
157415 14928 990692.984 69 90 990780.000 990655.170 0.01% 24.9 125s
163348 13906 cutoff 73 990780.000 990665.246 0.01% 24.8 130s
170321 12903 990687.161 71 70 990780.000 990677.548 0.01% 24.6 135s
Cutting planes:
Gomory: 4
Implied bound: 41
MIR: 1114
Flow cover: 148
Relax-and-lift: 1
Explored 173078 nodes (4253531 simplex iterations) in 136.97 seconds (178.34 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 990780 990780 990780 ... 990955
Optimal solution found (tolerance 1.00e-04)
Best objective 9.907800000000e+05, best bound 9.906827289231e+05, gap 0.0098%
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 8545 rows, 2232 columns and 23568 nonzeros
Model fingerprint: 0x23695c7b
Variable types: 672 continuous, 1560 integer (1560 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 4e+04]
Presolve removed 789 rows and 0 columns
Presolve time: 0.07s
Presolved: 7756 rows, 2232 columns, 21342 nonzeros
Variable types: 672 continuous, 1560 integer (1560 binary)
Found heuristic solution: objective 1125610.0000
Root relaxation: objective 9.882113e+05, 2064 iterations, 0.04 seconds (0.04 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 988211.330 0 159 1125610.00 988211.330 12.2% - 0s
H 0 0 1125004.0000 988211.330 12.2% - 0s
H 0 0 1124844.0000 988260.979 12.1% - 0s
0 0 989271.123 0 191 1124844.00 989271.123 12.1% - 0s
0 0 989386.545 0 193 1124844.00 989386.545 12.0% - 0s
0 0 990895.926 0 161 1124844.00 990895.926 11.9% - 0s
0 0 991137.821 0 189 1124844.00 991137.821 11.9% - 0s
0 0 991140.925 0 168 1124844.00 991140.925 11.9% - 0s
0 0 991675.199 0 151 1124844.00 991675.199 11.8% - 0s
0 0 991681.986 0 167 1124844.00 991681.986 11.8% - 0s
0 0 991681.986 0 183 1124844.00 991681.986 11.8% - 0s
0 0 991687.956 0 157 1124844.00 991687.956 11.8% - 0s
H 0 0 1123854.0000 991687.956 11.8% - 0s
H 0 0 1002725.0000 991721.598 1.10% - 0s
0 0 991721.598 0 139 1002725.00 991721.598 1.10% - 0s
0 0 991721.941 0 146 1002725.00 991721.941 1.10% - 0s
0 0 991722.506 0 121 1002725.00 991722.506 1.10% - 0s
0 0 991722.506 0 184 1002725.00 991722.506 1.10% - 0s
0 0 991724.839 0 167 1002725.00 991724.839 1.10% - 0s
H 0 0 1002550.0000 991724.839 1.08% - 0s
0 0 991730.492 0 184 1002550.00 991730.492 1.08% - 0s
0 0 991730.492 0 184 1002550.00 991730.492 1.08% - 0s
0 0 991732.122 0 169 1002550.00 991732.122 1.08% - 1s
0 0 991732.410 0 186 1002550.00 991732.410 1.08% - 1s
0 0 991732.410 0 210 1002550.00 991732.410 1.08% - 1s
0 0 991732.410 0 195 1002550.00 991732.410 1.08% - 1s
0 2 991732.410 0 195 1002550.00 991732.410 1.08% - 1s
H 32 38 1002275.0000 991734.343 1.05% 79.6 1s
H 99 103 995825.00000 991734.343 0.41% 84.9 1s
H 100 103 995405.00000 991734.343 0.37% 84.2 1s
H 107 110 995190.00000 991734.343 0.35% 80.4 1s
H 131 122 995020.00000 991734.343 0.33% 70.5 1s
H 139 126 994935.00000 991736.299 0.32% 67.6 1s
H 142 126 994725.00000 991736.299 0.30% 69.4 1s
H 172 151 994686.00000 991736.299 0.30% 60.7 1s
H 179 151 994649.00000 991736.299 0.29% 58.6 1s
H 205 167 994295.00000 991736.299 0.26% 56.4 2s
H 250 195 993980.00000 991736.299 0.23% 51.7 2s
H 434 213 993975.00000 991738.444 0.23% 44.2 2s
H 440 214 993965.00000 991738.444 0.22% 44.1 2s
* 1191 520 71 993889.00000 991955.089 0.19% 43.8 4s
H 1319 634 993864.78689 992003.841 0.19% 42.0 4s
H 1320 628 993855.60656 992003.841 0.19% 42.0 4s
H 1324 627 993854.90323 992003.841 0.19% 41.9 4s
* 1325 598 84 993812.00000 992003.841 0.18% 41.9 4s
H 1398 592 993810.00000 992014.838 0.18% 41.0 4s
1399 588 992911.797 11 195 993810.000 992014.838 0.18% 41.0 5s
1432 613 992024.257 15 190 993810.000 992024.257 0.18% 43.2 10s
4228 1126 993419.505 31 84 993810.000 993298.190 0.05% 29.5 15s
9645 1816 993718.259 52 19 993810.000 993498.621 0.03% 23.9 20s
15322 2680 993716.541 62 3 993810.000 993619.286 0.02% 21.8 25s
22535 3542 cutoff 48 993810.000 993660.000 0.02% 19.8 31s
27263 2973 993699.000 43 4 993810.000 993690.850 0.01% 19.8 35s
Cutting planes:
Gomory: 3
Lift-and-project: 3
Implied bound: 39
Clique: 3
MIR: 193
StrongCG: 2
Flow cover: 54
Zero half: 2
RLT: 8
Relax-and-lift: 3
Explored 31048 nodes (597858 simplex iterations) in 37.28 seconds (50.42 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 993810 993810 993812 ... 994686
Optimal solution found (tolerance 1.00e-04)
Best objective 9.938100000000e+05, best bound 9.937144285714e+05, gap 0.0096%
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 13081 rows, 2232 columns and 36204 nonzeros
Model fingerprint: 0xb9b1994c
Variable types: 672 continuous, 1560 integer (1560 binary)
Coefficient statistics:
Matrix range [3e-04, 6e+04]
Objective range [1e+00, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 4e+04]
Presolve removed 1356 rows and 0 columns
Presolve time: 0.10s
Presolved: 11725 rows, 2232 columns, 33438 nonzeros
Variable types: 672 continuous, 1560 integer (1560 binary)
Use crossover to convert LP symmetric solution to basic solution...
Extra simplex iterations after uncrush: 24
Root relaxation: objective 9.886341e+05, 647 iterations, 0.05 seconds (0.04 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 988634.126 0 157 - 988634.126 - - 0s
0 0 989023.535 0 180 - 989023.535 - - 0s
0 0 989055.255 0 164 - 989055.255 - - 0s
0 0 990551.330 0 171 - 990551.330 - - 0s
0 0 991373.775 0 164 - 991373.775 - - 0s
0 0 991374.390 0 167 - 991374.390 - - 0s
0 0 991670.808 0 147 - 991670.808 - - 0s
0 0 991675.326 0 156 - 991675.326 - - 0s
0 0 991676.496 0 188 - 991676.496 - - 0s
0 0 991677.001 0 184 - 991677.001 - - 1s
0 0 991716.134 0 193 - 991716.134 - - 1s
0 0 991736.808 0 221 - 991736.808 - - 1s
0 0 991737.544 0 230 - 991737.544 - - 1s
0 0 991744.334 0 227 - 991744.334 - - 1s
0 0 991745.433 0 234 - 991745.433 - - 1s
0 0 991751.361 0 228 - 991751.361 - - 1s
0 0 991751.916 0 243 - 991751.916 - - 1s
0 0 991756.829 0 241 - 991756.829 - - 1s
0 0 991759.393 0 261 - 991759.393 - - 1s
0 0 991761.125 0 246 - 991761.125 - - 1s
0 0 991762.178 0 263 - 991762.178 - - 1s
0 0 991762.354 0 244 - 991762.354 - - 1s
0 0 991769.273 0 246 - 991769.273 - - 1s
0 0 991769.468 0 258 - 991769.468 - - 1s
0 0 991804.075 0 234 - 991804.075 - - 1s
0 0 991804.789 0 227 - 991804.789 - - 1s
0 0 991805.409 0 227 - 991805.409 - - 1s
0 0 991805.431 0 238 - 991805.431 - - 1s
H 0 0 1001045.0000 991805.431 0.92% - 1s
H 0 0 1000905.0000 991805.454 0.91% - 2s
0 0 991805.454 0 232 1000905.00 991805.454 0.91% - 2s
0 0 991806.205 0 231 1000905.00 991806.205 0.91% - 2s
0 0 991806.364 0 229 1000905.00 991806.364 0.91% - 2s
0 0 991806.786 0 238 1000905.00 991806.786 0.91% - 2s
0 0 991806.898 0 235 1000905.00 991806.898 0.91% - 2s
0 0 991807.061 0 235 1000905.00 991807.061 0.91% - 2s
0 0 991807.061 0 235 1000905.00 991807.061 0.91% - 2s
0 2 991807.061 0 235 1000905.00 991807.061 0.91% - 2s
H 164 126 1000766.0000 991810.720 0.89% 166 4s
H 242 180 1000710.0000 991810.720 0.89% 154 4s
H 252 180 1000640.0000 991810.720 0.88% 149 4s
H 255 180 1000575.0000 991810.720 0.88% 153 4s
348 287 997213.162 9 197 1000575.00 991811.259 0.88% 135 5s
H 385 277 999950.00000 991811.259 0.81% 130 5s
H 386 274 999920.00000 991811.259 0.81% 131 5s
H 386 272 999612.00000 991811.259 0.78% 131 5s
H 391 267 999250.00000 991811.259 0.74% 130 5s
H 432 283 999240.00000 991811.259 0.74% 121 5s
H 465 248 998290.00000 991811.259 0.65% 115 5s
H 568 286 997935.00000 991924.397 0.60% 117 6s
H 576 281 997845.00000 991924.397 0.59% 119 6s
H 1011 535 997710.00000 991966.592 0.58% 100 7s
H 1012 528 997625.00000 991966.592 0.57% 100 7s
H 1016 517 997429.00000 991966.592 0.55% 101 7s
H 1026 358 996165.00000 991966.592 0.42% 100 8s
1039 359 993961.042 61 238 996165.000 991966.592 0.42% 98.8 10s
1078 386 infeasible 15 996165.000 992001.717 0.42% 101 16s
H 1137 397 995630.00000 994108.351 0.15% 102 17s
H 1171 388 995480.00000 994108.351 0.14% 100 17s
H 1175 369 995440.00000 994108.351 0.13% 100 17s
H 1201 374 995305.00000 994108.351 0.12% 98.8 17s
H 1203 357 995135.00000 994108.351 0.10% 98.7 17s
H 1205 341 995085.00000 994108.351 0.10% 98.6 17s
H 1208 326 994990.00000 994108.351 0.09% 98.3 17s
H 1242 320 994815.00000 994108.351 0.07% 96.3 18s
H 1275 307 994737.00000 994108.351 0.06% 94.3 18s
H 1319 286 994715.00000 994108.351 0.06% 91.8 18s
H 1378 258 994710.00000 994240.900 0.05% 89.0 18s
H 1497 261 994705.00000 994372.220 0.03% 84.3 19s
1867 320 994619.631 40 41 994705.000 994434.142 0.03% 72.1 20s
* 2182 352 58 994697.00000 994444.397 0.03% 64.4 20s
5024 519 cutoff 38 994697.000 994578.833 0.01% 39.0 25s
Cutting planes:
Gomory: 3
Implied bound: 42
Clique: 5
MIR: 164
Flow cover: 103
Zero half: 23
RLT: 14
Relax-and-lift: 2
Explored 5909 nodes (215369 simplex iterations) in 25.70 seconds (31.61 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 994697 994705 994710 ... 995305
Optimal solution found (tolerance 1.00e-04)
Best objective 9.946970000000e+05, best bound 9.946060555556e+05, gap 0.0091%